"App Stores"

Aptoide — An alternative, decentralized set of repos that inspired F-Droid, for those who still want mainstream apps and timely updates without having to sign in to Google or sideload apks repeatedly. It features malware scanning and compares the app signature with that of the Google Play Store when available.

You can also download APK files directly from Google Play with Evozi's APK Downloader or APK Downloader, APKPure or Yalp Store. Be wary of third party sources that claim to provide unmodified APKs from Google Play if an app signature, checksum or other means of verification is not available. Some may bundle in malware or adware.

ApkTrack — Well, it's not an app store, but it scrapes a couple of sites for updates for apps you have installed, and gives you the direct .apk download for them. Useful for people who use proprietary software (e.g. Nova Launcher, KLWP), but want to avoid using the Play Store. One could argue that it's useless when Aptoide (with its verification and whatnot) already exists, but it never hurts to have more alternatives.

4chan

8chan

Communications

Signal — The successor of TextSecure and RedPhone. It provides end-to-end encrypted VoIP and IM over Wi-Fi or cellular internet using your existing phone number. It is recommended by both Snowden and Bruce Schneier. Requires Google Play Services.

Silence — Send encrypted SMS messages. Fork of TextSecure with only the SMS encryption and no internet messaging. Available in Google, Amazon and F-Droid App Store.

Music

BlackPlayer — A favorite among many /g/entoomen, it is a player light on resources, light on the eyes, but not light on functionality!

Phonograph — A music player with customization capabilites for appearance.

PowerAMP — Trial version, but may be worth the money for the extra features.

GoneMAD Music Player — Know the recently released Foobar2000 for Android? This app more or less is what its' devs are trying to recreate - and they can't do it, despite the fact that it was in development for years. Supports a shitload of formats including .opus(!!), and it has a decent UI, which is reminiscent of Vanilla Player and Rocket Player combined. Good, robust app. It's paid, though - the free version is a 14 day trial.

Vanilla Music — A FOSS music player, for those with tinfoil wrapped phones.

Timber (Currently in beta, so it may have bugs!) — Another open-source player with modern, material inspired design. Comparable to Phonograph in terms of settings.

Video players

MX Player — A solid player. Will play nearly everything (some formats will require a custom codec), really good subtitle support. Proprietary and ad-supported.

VLC — Android version of the vastly popular VLC client. Plays everything.

MPV — An unofficial experimental build of /g/'s favorite player mpv. Suggested for those who want a FOSS video player, but doesn't like VLC. Remember these builds are experimental and might not work very good

YouTube

NewPipe — A lightweight YouTube front end without the botnet. Can download videos for offline viewing, play audio in background, but cannot view comments. It is under heavy development.

Skytube — YouTube client with HW acceleration, subscribe to channels without an account.

Keepass2Android — a modern version of KeePass for Android. Has an integrated keyboard (to avoid other apps from logging your password in your clipboard), and fingerprint unlocking. Not on F-Droid, but it's open source.

Ad-blockers

Adguard — Works as a local VPN. Also battery hungry, but lets you use a firewall even if you don't have root, and can filter mobile traffic.

DNS66 — Blocking host names through DNS. Can be used for ad-blocking. Best part is that it doesn't require root, or fucking around with proxy settings like in AdBlock Plus. Worst part is that it's got a couple of issues. Be a good /g/entoomen and help the dev find and squash bugs, or suggest features.

Games

Before you install any games from the Play Store, read over their permissions! A lot of free to play games will run in the background, feed you ads, and data mine the shit out of you. If you have the right security on your phone, you can easily block snoopy permissions and enjoy the terrible free to play game.

Miscellaneous

AntennaPod — An Excellent podcast manager that is available on F-Droid.

Material Tea Timer — A fucking material tea-timer so you can have your tea tasting just right, ensuring peak coziness in the cold during months. Cafe de Touhou is also recommended playing in the background.

Survival Manual — Learn how to survive innawoods. А great companion for both veterans and newbies alike. Hell, it's a good read even if you're not going anywhere. Guide is based on the (public domain) US Army Survival Field-Manual FM 21-76, and is fully working offline. Even has illustrations.

microG — FOSS re-implementation of Google’s proprietary Android user space apps and libraries. Great for those who desire a bit more privacy, but still want to continue using Google's services. When used on older phone, it can even better your battery life. (Your ROM needs to support signature spoofing - Omni 5 and 6 have it in out of the box, but other ROMs require a patch. If you're not comfortable with running xposed, or just want to avoid it for some reason, you can use Needle by moosd). Implementation status can be viewed here.